I've done exactly the same thing for a number of people, but my technique is a bit different -- because I don't own a .22 handgun.
I always start people with a revolver. It's heavy, but is easy to control. It's easy to operate, and I use it to make sure they are holding it correctly. I've seen novices hurt themselves badly because they forgot the slide on a semi-auto slams back when you fire.
My carry gun is a S&W stainless .357 Model 641. I tried shooting a .380 a couple of years ago, found that it tended to jam, the magazine was difficult to load, and the slide nicked my left thumb on the way back, a problem I never had with the slide on my Beretta .40. In short, I vastly prefer the hammerless S&W as a carry gun over a .380, even though the S&W only has five shots.